+0  
 
0
265
1
avatar

A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres 

Guest Feb 22, 2018

Best Answer 

 #1
avatar+20009 
+1

A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres 

 

\(\begin{array}{|lcll|} \hline V_{\text{cylinder}} &=& \pi r^2\times 6r \\ &=& 6\pi r^3 \\\\ V_{\text{$3\ $spheres }} &=& 3\times \frac43\pi r^3 \\ &=& 4\pi r^3 \\\\ 1 - \dfrac{4\pi r^3}{6\pi r^3} \\\\ = 1 - \dfrac{2}{3} \\\\ = \dfrac{1}{3} \\ \hline \end{array} \)

 

\(\text{$\frac13$ of the cylinder is not filled by the spheres.} \)

 

laugh

heureka  Feb 22, 2018
 #1
avatar+20009 
+1
Best Answer

A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres 

 

\(\begin{array}{|lcll|} \hline V_{\text{cylinder}} &=& \pi r^2\times 6r \\ &=& 6\pi r^3 \\\\ V_{\text{$3\ $spheres }} &=& 3\times \frac43\pi r^3 \\ &=& 4\pi r^3 \\\\ 1 - \dfrac{4\pi r^3}{6\pi r^3} \\\\ = 1 - \dfrac{2}{3} \\\\ = \dfrac{1}{3} \\ \hline \end{array} \)

 

\(\text{$\frac13$ of the cylinder is not filled by the spheres.} \)

 

laugh

heureka  Feb 22, 2018

4 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.